c++ - Floating Point, how much can I trust less than / greater than comparisons? -

let's have 2 floating point numbers, , want compare them. if 1 greater other, program should take 1 fork. if opposite true, should take path. , should same thing, if value being compared nudged in direction should still make compare true.

it's difficult question phrase, wrote demonstrate -

float = random(); float b = random();  // returns number (no infinity or nans)  if(a < b){     if( !(a < b + float_episilon) ) launchthemissiles();     buildhospitals();  }else if(a >= b){     if( !(a >= b - float_episilon) ) launchthemissiles();     buildorphanages();  }else{     launchthemissiles();  // should never called, in branch } 

given code, launchthemissiles() guaranteed never called?

if can guarantee a , b not nans or infinities, can do:

if (a<b) {     … } else {     … } 

the set of floating point values except infinities , nans comprise total ordering (with glitch 2 representations of zero, shouldn't matter you), not unlike working normal set of integers — difference magnitude of intervals between subsequent values not constant, integers.

in fact, ieee 754 has been designed comparisons of non-nan non-infinity values of same sign can done same operations normal integers (again, glitch zero). so, in specific case, can think of these numbers of “better integers”.